Question

What line is parallel to `y=-3x+4` and has an `x`-intercept at 4?

Answer 1

See a solution process below:

Explanation:

If the second line is parallel to the line in the problem then it has the same slope as the line in the problem.

The line in the problem is in slope-intercept form. The slope-intercept form of a linear equation is: `y = color(red)(m)x + color(blue)(b)`

Where `color(red)(m)` is the slope and `color(blue)(b)` is the y-intercept value.

`y = color(red)(-3)x + color(blue)(4)`

Therefore, the slope of the line is `color(red)(m = -3)`

We also know a point on the second line the x-intercept at 4 or:

`(4, 0)`

We can now use the point slope formula to write and equation for the second line. The point-slope form of a linear equation is: `(y - color(blue)(y_1)) = color(red)(m)(x - color(blue)(x_1))`

Where `(color(blue)(x_1), color(blue)(y_1))` is a point on the line and `color(red)(m)` is the slope.

Substituting gives:

`(y - color(blue)(0)) = color(red)(-3)(x - color(blue)(4))`

We can now transform this to slope-intercept form:

`y = (color(red)(-3) xx x) - (color(red)(-3) xx color(blue)(4))`

`y = -3x - (-12)`

`y = -3x + 12`